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Uniform constants in Hausdorff-Young inequalities for the Cantor group model of the scattering transform
Uniform constants Hausdorff-Young inequalities Cantor group model scattering transform
2011/1/21
Analogues of Hausdorff-Young inequalities for the Dirac scattering transform (a.k.a. SU(1, 1) nonlinear Fourier transform) were first established by Christ and Kiselev [1],[2]. Later Muscalu, Tao, and...
Stability of the solution to inverse obstacle scattering problem
inverse obstacle scattering problem math
2010/11/1
It is proved that if the scattering amplitudes at a fixed wavenumber for two obstacles from a certain large class of obstacles differ a little, than the obstacles differ a little. Error estimate is g...
On the wave operators and Levinson's theorem for potential scattering in R^3
wave operators Levinson's theorem potential scattering
2010/12/13
The paper is a presentation of recent investigations on potential scattering in R3. We advocate a new formula for the wave operators and deduce the various outcomes that follow
from this formula. A t...
Uniqueness theorems for inverse obstacle scattering in Lipschitz domains
Uniqueness theorems inverse obstacle scattering in Lipschitz domains
2010/11/1
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. T...